Gaps and Well-Composed Objects in the Triangular Grid
We extend the notion of a gap from the square to the triangular grid, and we propose a possible classification of gaps in this grid. We give four definitions of well-composed objects in the triangular grid by translating the existing definitions of such objects in the square grid. We show that these definitions in the triangular grid are equivalent, as they are in the square grid.
We give a formula relating the number of gaps of different types in an object in this grid with the number of boundary cells in the object, as well as three short intuitive proofs of this formula.
KeywordsDigital topology Triangular grid Gaps Well-composedness
We are grateful to the anonymous reviewers for careful reading of the paper and constructive comments. This work has been partially supported by the Ministry of Education and Science of the Republic of Serbia within the Project No. 34014.
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